Currently, our main research focuses on the study of "rough sets". Our approach consists on using Category Theory to implement rough sets.
Within the abstract framework provided by Category Theory, we study some structures aiming a solid background for the developing of a general framework for unification. In particular we work with sets of terms. Monads, in these context, represent a foundamental point in our research. We have studied how monads can be used to generalise and interpret rough situations. In particular we have shown how the partially ordered monad contains enough structure to provide rough operations. In order to define rough approximations, we use the natural transformations in the monad. The specific properties of partially ordered monads guarantee the equivalence to the classical rough situation and, at the same time, provide an enviroment for the study of a more general situation. In this sense, the study of rough sets from a categorical point of view, simplifies the definitions and opens the doors to new conexions.
- P. Eklund, M.A. Galán, J. Karlsson
Categorical Innovations for Rough Sets. Studies in Computational Intelligence, Springer-Verlag Series. Acepted, To appear 2008.
Journal papers, ENTCS and LNAI:
Conference papers (refereed):